Abstract

Flow resistance caused by vegetation is a key parameter to properly assess flood management and river restoration. However, quantifying the friction factor or any of its alternative metrics, e.g. the drag coefficient, in canopies with complex geometry has proven elusive. We explore the effect of canopy morphology on vegetated channels flow structure and resistance by treating the canopy as a porous medium characterized by an effective permeability, a property that describes the ease with which water can flow through the canopy layer. We employ a two-domain model for flow over and within the canopy, which couples the log-law in the free layer to the Darcy-Brinkman equation in the vegetated layer. We validate the model analytical solutions for the average velocity profile within and above the canopy, the volumetric discharge and the friction factor against data collected across a wide range of canopy morphologies encountered in riverine systems. Results indicate agreement between model predictions and data for both simple and complex plant morphologies. For low submergence canopies, we find a universal scaling law that relates friction factor with canopy permeability and a rescaled bulk Reynolds number. This provides a valuable tool to assess habitats sustainability associated with hydro-dynamical conditions.

Abstract

One of the most significant challenges faced by hydrogeologic modelers is the disparity between the spatial and temporal scales at which fundamental flow, transport, and reaction processes can best be understood and quantified (e.g., microscopic to pore scales and seconds to days) and at which practical model predictions are needed (e.g., plume to aquifer scales and years to centuries). While the multiscale nature of hydrogeologic problems is widely recognized, technological limitations in computation and characterization restrict most practical modeling efforts to fairly coarse representations of heterogeneous properties and processes. For some modern problems, the necessary level of simplification is such that model parameters may lose physical meaning and model predictive ability is questionable for any conditions other than those to which the model was calibrated. Recently, there has been broad interest across a wide range of scientific and engineering disciplines in simulation approaches that more rigorously account for the multiscale nature of systems of interest. In this article, we review a number of such approaches and propose a classification scheme for defining different types of multiscale simulation methods and those classes of problems to which they are most applicable. Our classification scheme is presented in terms of a flowchart (Multiscale Analysis Platform), and defines several different motifs of multiscale simulation. Within each motif, the member methods are reviewed and example applications are discussed. We focus attention on hybrid multiscale methods, in which two or more models with different physics described at fundamentally different scales are directly coupled within a single simulation. Very recently these methods have begun to be applied to groundwater flow and transport simulations, and we discuss these applications in the context of our classification scheme. As computational and characterization capabilities continue to improve, we envision that hybrid multiscale modeling will become more common and also a viable alternative to conventional single-scale models in the near future.

Abstract

Many studies in the last decade have revealed that patterns at the microscale can reduce skin drag. Yet, the mechanisms and parameters that control drag reduction, e.g. Reynolds number and pattern geometry, are still unclear. We propose an effective medium representation of the micro-features, that treats the latter as a porous medium, and provides a framework to model turbulent flow over patterned surfaces. Our key result is a closed-form expression for the skin friction coefficient in terms of frictional Reynolds (or Kármán) number in turbulent regime, the viscosity ratio between the fluid in and above the features, and their geometrical properties. We apply the proposed model to turbulent flows over superhydrophobic ridged surfaces. The model predictions agree with laboratory experiments for Reynolds numbers ranging from 3000 to 10000.

Abstract

In this work we use a multiscale framework to calculate the fluidization threshold of three-dimensional cohesive granulates under shear forces exerted by a creeping flow. A continuum model of flow through porous media provides an analytical expression for the average drag force on a single grain. The balance equation for the forces and a force propagation model are then used to investigate the effects of porosity and packing structure on the stability of the pile. We obtain a closed-form expression for the instability threshold of a regular packing of monodisperse frictionless cohesive spherical grains in a planar fracture. Our result quantifies the compound effect of structural (packing orientation and porosity) and dynamical properties of the system on its stability.

Abstract

We consider transport of a solute that undergoes a nonlinear heterogeneous reaction: after reaching a threshold concentration value, it precipitates on the solid matrix to form a crystalline solid. The relative importance of three key pore-scale transport mechanisms (advection, molecular diffusion, and reaction) is quantified by the Péclet (Pe) and Damköhler (Da) numbers. We use multiple-scale expansions to upscale a pore-scale advection-diffusion equation with reactions entering through a boundary condition on the fluid-solid interface, and to establish sufficient conditions under which macroscopic advection-dispersion-reaction equations provide an accurate description of the pore-scale processes. These conditions are summarized by a phase diagram in the (Pe, Da)-space, parameterized with a scale-separation parameter that is defined as the ratio of characteristic lengths associated with the pore- and macro-scales.

Abstract

The ability to determine static and (hydro)dynamic properties of carbon nanotubes (CNTs) is crucial for many applications. While their static properties (e.g., solubility and wettability) are fairly well understood, their mechanical responses (e.g., deflection under shear) to ambient fluid flow are to a large extent unknown. We analyze the elastic response of single-walled CNT forests, attached to the bottom wall of a channel, to the aerodynamic loading exerted by both laminar and turbulent flows. Our analysis yields analytical expressions for velocity distributions, the drag coefficient, and bending profiles of individual CNTs. This enables us to determine flexural rigidity of CNTs in wind-tunnel experiments. The model predictions agree with laboratory experiments for a large range of channel velocities.